1. Field of the Invention
The present invention relates to a course control method for a composite system constituted by a plurality of control systems for generating control inputs for causing controlled objects to follow up desired target values (courses).
2. Related Background Art
A course control method of this type has been applied to various numerical control apparatuses and the like. For example, in machine tools, the above-mentioned course control method is used for position/course control.
FIG. 31 is a block diagram showing a position control system model for a machine tool. Such a control system is arranged for each axis to constitute a composite control system such as the one shown in FIG. 32.
Referring to FIG. 31, a position command value generation means 1 inputs a target value (course) to a control means 2. A controlled object 3 feeds back a controlled amount corresponding to a control input, supplied from the control means 2, to another system or the control means 2. The control means 2 has gains Wo and Wc/K and a transfer coefficient Wa/s. The controlled object 3 has transfer coefficients K/S and 1/S.
Referring to FIG. 32, position command value generation means 1a and 1b are arranged for the respective axes to input target values to control means 2a and 2b for the respective axes. Controlled objects 3a and 3b for the respective axes feed back controlled amounts corresponding to control inputs, supplied from the control means 2a and 2b, to other systems or the control means 2a and 2b.
As described above, in a conventional machine tool, provided that a circular trace is to be drawn with reference to two axes, each position control system is constituted by the position command value generation means 1, the controlled object 3, and the control means 2. Each position command value generation means 1 outputs a target position/course command signal. The controlled object has a drive means to physically move. Each control means 2 receives a position command value for each axis component from the position signal generation means 1 and a state amount representing the state of the controlled object 3 and outputs a control input to the controlled object 3 constituted by the corresponding drive means.
When, therefore, position command values for the respective axis components are output from the position command value generation means 1a and 1b, the corresponding controlled objects are simultaneously position-controlled by the control means 2a and 2b for the respective axes, thereby drawing a circular trace. As shown in FIG. 31, the position control system for each axis is a control system having a position control loop having a relatively low gain and a velocity control loop located inside the position control loop and having a relatively high gain. This control system is characterized in that high rigidity can be set against disturbances owing to the high gain of the velocity control loop, and a response without excessive impact on a mechanical system can be easily obtained owing to the low gain of the position control loop. Furthermore, by providing integration characteristics for a compensator of the velocity control loop, the rigidity against disturbances can be greatly increased, thereby eliminating positional errors with respect to stepwise torque disturbances.
FIG. 33 is a block diagram showing a position control system model of a conventional numerical control apparatus.
Referring to FIG. 33, a target value generation means 11 outputs target positions 12a and 12b associated with the respective control axes to control means 13a and 13b. Controlled objects 14a and 14b corresponding to the respective axes output controlled amounts 15a and 15b based on control inputs from the control means 13a and 13b. In addition, referring to FIG. 33, a position control system and a velocity control system have loop gains Wo and Wc, respectively, and a constant K is determined by the inertia of a drive system and the gain of a driver.
First, the target value generation means 11 calculates target positions corresponding to the respective control axes in accordance with a target course and a target velocity. Position control systems for the respective axes are then formed to follow up the target values, and are independently controlled for the respective axes. When the synchronous relationship between course command values for the respective axes, supplied as target values, are accurately maintained, and the control feed amounts of the respective axes are sufficiently small in a follow-up operation, target course control can be performed by this method.
FIG. 34 is a schematic view showing an axial feed control system of a conventional position control apparatus.
Referring to FIG. 34, a position 32 of the X axis indicates the distance between the centrobaric position of an X axis movable member 35 and an external reference point 31, and a position 33 of the Y axis indicates the distance between the centrobaric position of a Y axis movable member 36 and the centrobaric position of the X axis. A position 3 of the Z axis indicates the distance between the centrobaric position of the Y axis movable member 36 and the external reference position 31. Control inputs are thrusts 37 and 38 acting on the X and Y axis movable members 35 and 36 in the horizontal direction. In practice, the thrusts 37 and 38 are obtained by supplying power to linear motors or the like.
It is an object of the positioning apparatus for controlling such a composite system to cause the Z axis to reach a target position as soon as possible with limited power and quickly eliminate the influence of disturbances on the Z axis when the disturbances act on the system.
FIG. 35 is a block diagram showing a control arrangement in the axial feed control system of the position control apparatus shown FIG. 34. The operation of the arrangement will be described below.
When a target value generation means 41 outputs a target value signal 42 as a position target value for the Z axis, a coarse feed X axis 52a starts to move, and a position (X axis controlled amount) 50a as a controlled amount moves close to the target value. In this case, when a positional error (X axis error signal) 44 becomes smaller than a set value, a determination means 43 supplies the current positional error 44, as a position command value (Y axis target value), to a Y axis 52b. If the positional error 44 is larger than the set value, the position command value 45 to the Y axis becomes "0". The Y axis moves to coincide with the position command value 45. As a result, a Z axis controlled amount 54 as the sum of the X axis controlled amount 50a and a Y axis controlled amount 50b coincides with the position target value 42 for the Z axis.
In a controller 55, the following are set: a Y axis error signal 46, an X axis compensator 47a, a Y axis compensator 47b, an X axis control input 48a, a Y axis control input 48b, an X axis controlled object 49a, a Y axis controlled object 49b, a controlled amount 50b, an X axis velocity 51a, and a Y axis velocity 51b.
Although the adder (determination means) 43 exists conceptually but does not exist in the actual control system. The controller 55 has gains Wo1, Wo2, M1, and M2 and transfer functions K1/S, K2/S, and 1/S.
FIG. 36 shows the response characteristics of the axial feed control system of the position control apparatus shown in FIG. 35. Referring to FIG. 36, the abscissa indicates time (msec); and the ordinate, target values. Note that the target value for the Z axis changes in the form of a ramp, and the final value is "10".
As shown in FIG. 36, when the determination means 43 is set such that the Y axis starts to move when the positional error becomes 0.21, it takes about 36 (msec) for the Z axis to reach 0.2% of the target value. The maximum accelerations required for the movement in this case are 1,834 (rad/sec.sup.2) for the X axis and 1,284 (rad/sec.sup.2) for the Y axis. The maximum accelerations are substantially proportional to the power required to move the axes. Since the power which can be normally used is limited, the accelerations must be minimized. In addition, since a vibration produced by a mechanical system is proportional to an acceleration, the maximum accelerations must be minimized.
In the above-described position control method, however, the following problems are posed. 1 The method is based on the assumption that the response speeds of the respective axes are completely the same. 2 In order to increase the course precision, the gain of the position control loop must be set to be high. 3 In order to obtain high rigidity against disturbances, the gain of the velocity control loop must be set to be high.
These problems posed in the conventional position control method when course control of a position control system is performed by using two axes, i.e., the X and Y axes, will be described in detail below with reference to an X-Y plotter with two orthogonal axes and the like.
In order to draw a circle on a plane defined by two straight axes, i.e., the X and Y axes, for example, a sine (sin) wave and a cosine (cos) wave are given, as position target values, to the X and Y axes. An accurate circle can be drawn by causing the X and Y axes to perfectly follow up these target values.
FIG. 37 is a chart showing traces drawn by an X-Y plotter with two orthogonal axes to which the conventional position control method is applied.
As shown in FIG. 37, a trace C0 is a target circular trace. In the conventional method, the response speeds of the X and Y axes are set to be the same value. When the position control loop gains for the X and Y axes are set to be the same, as described above, a trace C1 is obtained. The trace C1 becomes a circular trace, although it has a radius smaller than that of the target circle except at the start and end points. In order to examine the problem 1, the position control loop gains of the X and Y axes are set to be different values to perform course control upon changing the response speeds of the X and Y axes. In this case, a trace C2 is obtained. As is apparent, the trace C2 does not coincide with the target circle but becomes an ellipse. It is understood from this example why the X and Y axes need to have the same response speed.
The relationship between the course precision and the gain of the position control loop, which corresponds to the problem 2, will be examined below. Assume that the X and Y axes have the same response speed. In this case, the trace C1 is obtained, which is a follow-up trace corresponding to a target course set when the response speeds of the X and Y axes are the same. In this example, the follow-up trace also causes an error with respect to the target circle. In this case, if the course error between the target circular course and the follow-up trace in a normal state is represented by a radius reduction amount dR, dR=Vo.sup.2 /2RWo.sup.2 (where Vo is the velocity, R is the radius, and Wo is the position loop gain). Therefore, when a circle is to be drawn upon setting a circle defined by the velocity Vo and the radius R as a target trace, the course error is reduced in inverse proportion to the square of the position loop gain Wo. In other words, in order to draw a circle with high precision, a gain Wc of the velocity control loop inside the position control loop must be set to be high.
In general, however, when the gain of the velocity control loop is set to be high, vibration of the mechanical system is caused. For this reason, the gain cannot be set to be higher than a given value. Therefore, it is difficult to set a high position loop gain, and it is more difficult to make the precision of a trace fall within a target course error as the velocity of a target circular trace is increased and the radius of the circle is decreased.
The problem 2 will be examined next with reference to FIG. 38.
FIG. 38 is a chart showing traces drawn by an X-Y plotter with two orthogonal axes to which the conventional position control method is applied, when disturbances are applied.
Referring to FIG. 38, a trace C0 is a target circular trace, and a trace C1 is a trace drawn when no disturbances are present. A trace C2 is a response trace obtained when a stepwise acceleration disturbance is applied to the X axis while a circle is drawn. As indicated by the trace C2, when disturbances are applied to a controlled object, the course error is increased. A trace C3 is a response trace obtained when the gain of the velocity control loop of the same system is doubled. In this case, the course error with respect to the same acceleration disturbance is smaller than that of the trace C2, indicating that an increase in velocity loop gain leads to the suppression of disturbances.
As has been described above, however, the gain of the velocity control loop is limited because an increase in gain causes vibration of the mechanical system. In addition, as the gain of the velocity control loop is increased, the acceleration required to suppress disturbances increases. Therefore, it is very difficult to perform course control with high precision while suppressing the influence of disturbances.
In order to perform course control with higher precision by the control method in the numerical control apparatus shown in FIG. 33, the loop gain of the position control system needs to be increased or a feed forward control system needs to be formed to improve the follow-up characteristics of a servo system. If, however, the follow-up characteristics of the servo system are improved, the following new problems are posed. That is, the capacity of a motor driver is increased, and high-frequency vibration is caused in a mechanical system, resulting in a deterioration in positional precision.
For this reason, an increase in precision must be realized without using large accelerations, and hence high-speed, high-precision course control needs to be performed by properly accelerating/decelerating the apparatus without using an excessive torque. When a simple straight light or curve is to be drawn, only a simple calculation is required, and it is relatively easy to properly increase/decrease a target value. However, it is difficult to properly increase/decrease a target value and perform high-speed, high-precision course control when a free curve, a straight line, and a curve are connected to each other complicatedly. In this case, in properly accelerating/decelerating the apparatus, it is important to reduce not only the maximum accelerations but also vibration components included in the acceleration components.
If a satisfactory response speed cannot be obtained in the two-axis control system shown in FIG. 36, the gains (Wo1, Wo2, M1, and M2) of the control system shown in FIG. 35 must be increased to increase the response speed and improve the rigidity. However, with an increase in gain, the maximum accelerations required for movement increase, requiring large power. In addition, when the gains are set to be high, the frequency band of the control system is expanded, causing vibration of the mechanical system. As a result, the convergence characteristics with respect to a target value may deteriorate. Furthermore, this arrangement requires a switching operation near a positional error determination value. Under certain conditions, this switching may cause self-excited oscillation. In this case, the convergence characteristics with respect to a target value deteriorate.
In conventional control apparatuses, such as a position control apparatus, a velocity control apparatus, and a temperature control apparatus, a plurality of controlled objects to be simultaneously controlled are present in a composite state. Various types of control operations are performed to cause such a composite control system to reach a target value at a high speed with limited power. For example, a position control apparatus has a control system for a composite system such as the one shown in FIG. 45, in which the first axis for coarse feed and the second axis for fine feed are respectively defined as the X and Y axes, and the Z axis is an axis indicating a position where the X and Y axes are synthesized. Control in such a position control apparatus will be described below.
FIG. 45 is a schematic view showing an axis feed control system of a conventional position control apparatus.
Referring to FIG. 45, a position 2 of the X axis indicates the distance between the centrobaric position of an X axis movable member 5 and an external reference point 1, and a position 3 of the Y axis indicates the distance between the centrobaric position of a Y axis movable member 6 and the centrobaric position of the X axis. A position 4 of the Z axis indicates the distance between the centrobaric position of the Y axis movable member 6 and the external reference point 1. In addition, control inputs are thrusts 7 and 8 acting on the X and Y movable members 5 and 6 in the horizontal direction. In practice, the thrusts 7 and 8 are obtained by supplying power to linear motors or the like.
It is an object of the positioning apparatus for controlling such a composite system to cause the Z axis to reach a target position as soon as possible with limited power and quickly eliminate the influence of disturbances on the Z axis when the disturbances act on the system.
FIG. 46 is a block diagram showing the first control arrangement in the axial feed control system of the position control apparatus shown in FIG. 45. The operation of the arrangement will be described below.
Upon reception of a target value signal 12, as a position target value for the Z axis, from a target value generation means 11, an X axis 22a for coarse feed starts to move, and a position (X axis controlled amount) 20a as a controlled amount moves close to the target value. In this case, when a positional error (X axis error signal) 14 becomes smaller than a given set value, a determination means 13 supplies the current positional error 14, as a position command value (Y axis target value) 15, to a Y axis 22b. When the positional error 14 is larger than the set value, the position command value 15 to the Y axis becomes "0". The Y axis 22b moves in accordance with the position command value 15. As a result, a Z axis controlled amount 24 as the sum of an X axis controlled amount 20a and a Y axis controlled amount 20b coincides with the position target value 12 associated with the Z axis.
In a controller 25, the following are set: a Y axis error signal 16, an X axis compensator 17a, a Y axis compensator 17b, an X axis control input 18a, a Y axis control input 18b, an X axis controlled object 19a, a Y axis controlled object 19b, a Y axis controlled amount 20b, an X axis velocity 21a, and a Y axis velocity 21b.
Although the adder 13 (determination means) exists conceptually but does not exist in the actual control system. The controller 25 has gains Wo1, Wo2, M1, and M2 and transfer functions K1/S, K2/S, and 1/S.
FIGS. 47 and 48 show the response characteristics of the axial feed control system of the position control apparatus shown in FIG. 46. Referring to FIGS. 47 and 48, the abscissa indicates time (msec); and the ordinate, target values. Note that these graphs respectively correspond to cases where target values associated with the Z axis are set to be "1" and "10".
As shown in FIG. 47, if the determination means 13 is set such that the Y axis starts to move when the positional error becomes 0.01, it takes about 30 (msec) for the Z axis to reach 0.1% of the target value. In this case, the maximum accelerations required for the movement are 1,600 (rad/sec.sup.2) for the X axis and 1,870 (rad/sec.sup.2) for the Y axis. The maximum accelerations are substantially proportional to the power required to move the axes. Since the power which can be normally used is limited, the accelerations must be minimized. In addition, since a vibration produced by a mechanical system is proportional to an acceleration, the maximum accelerations must be minimized. Furthermore, this arrangement requires a switching operation near a positional error determination value. Under certain conditions, this switching may cause self-excited oscillation. In this case, the convergence characteristics with respect to a target value deteriorate.
As shown in FIG. 48, if the determination means 13 is set such that the Y axis starts to move when the positional error becomes 0.21, it takes about 30 (msec) for the Z axis to reach 0.1% of the target value. In this case, the maximum accelerations required for the movement are 2,300 (rad/sec.sup.2) for the X axis and the 2,500 (rad/sec.sup.2) for the Y axis.
The behavior of the control system against disturbances will be described below with reference to FIGS. 49 and 50.
FIG. 49 is a block diagram showing the second control arrangement in the axial feed control system of the position control apparatus shown in FIG. 45. The same reference numerals in FIG. 49 denote the same parts as in FIG. 46.
Referring to FIG. 49, disturbances 26a and 26b are respectively applied to the X and Y axes.
FIG. 50 is a graph showing the behavior of the axial feed control system of the position control apparatus shown in FIG. 46 against the disturbances. Referring to FIG. 50, the abscissa indicates time (sec); and the ordinate, target values. Note that this graph corresponds to a case where a target value associated with the Z axis is set to be "10".
When, for example, any force is applied, as the disturbance 26a, to an X axis 22a, the velocity and position of the X axis 22a as a controlled object deviate from a target position and a target velocity owing to the disturbance 26a, thus causing a deviation. In this case, the control system operates in the same manner as in the case where a deviation is caused when a target value is applied. More specifically, an X axis compensator 17a generates a thrust to reduce this deviation to "0", thus moving the X axis 22a. When the positional error of the X axis 22a becomes smaller than a set value in a determination means 13, the Y axis starts to move, thus quickly reducing the deviation caused by the disturbance to "0". As shown in FIG. 50, for example, when the stepwise disturbance 26a is applied to the X axis 22a, the X axis 22a operates to reduce the positional error to "0" by itself at first. At time 0.175 (sec), a stepwise disturbance is applied to the X axis, and the X axis operates to reduce the positional error to "0" by itself at first. At around time 0.3 (sec), the positional error becomes smaller than the set value in the determination means 13, and the X axis starts to move.
Since control of the conventional composite system is performed in the above-described manner, if the satisfactory response speed, rigidity, and the like cannot be obtained with the response characteristics shown in FIG. 47, the gains Wo1, Wo2, M1, and M2 of the control system are increased to obtain a satisfactory response speed, rigidity, and the like. If, however, the above-mentioned gains Wo1, Wo2, M1, and M2 are increased, the frequency band of the control system is expanded to cause vibration of the mechanical system, resulting in a deterioration in convergence characteristics with respect to a target value. In addition, this arrangement requires a switching operation near a positional error determination value. Under certain conditions, this switching may cause self-excited oscillation, causing a deterioration in convergence characteristics with respect to a set target value. It is, therefore, difficult to increase the response speed and improve rigidity in control of the composite system.
In addition, if the satisfactory response speed and rigidity cannot be obtained with the response characteristics with respect to the disturbance shown in FIG. 49, the gains Wo1, Wo2, M1, and M2 of the control system are increased to obtain a satisfactory response speed, rigidity, and the like. If, however, the gains Wo1, Wo2, M1, and M2 are increased, the maximum accelerations required for the movement are increased, requiring large power. Furthermore, similar to the above-described case, if the gains are increased, vibration of the mechanical system is caused, and convergence characteristics with respect to a target value deteriorate. It is, therefore, difficult to increase the response speed and improve rigidity with respect to disturbances in control of the composite system.